Question

The number of five digit numbers having at least one of their digits repeated is:

Answer 1

no. of 5 digit no. of at least 1 digit repeated is same as

total possibility $-$ no digit repeat

$\Rightarrow 1^{st}$ Place can't contain '0' $\therefore$ no of ways $=96$ all other

has 10 ways to fill places.

If no digit respect $\Rightarrow 1^{st}$ place has 9 ways ; 2${}^{rd}$ place has

9 ways ; $3^{rd}$ has 8; 4${}^{th}$ both has ${}^{\prime }{7}^{\prime }$ 6 5 thy has '6' place

$\therefore$ total ways $=[9\times 10\times 10\times 10\times 10-(9\times 9\times 8\times 7\times 6\left)\right]=62784$